Intuitionistic fuzzy number and its arithmetic operation. In this paper, we develop interval valued intuitionistic fuzzy ivif confidence intervals for population mean, population proportion, differences in means of two populations, and differences in proportions of two populations. This paper proposes an improved score function for the effective ranking order of intervalvalued intuitionistic fuzzy sets ivifss and an intervalvalued intuitionistic fuzzy topsis method based on the score function to solve multicriteria decisionmaking problems in which all the preference information provided by decisionmakers is expressed as intervalvalued intuitionistic fuzzy decision. Interval valued intuitionistic fuzzy multicriteria decision making next, some basic definitions of intuitionistic fuzzy sets and interval valued intuitionistic fuzzy sets are provided 7, 8. Intuitionistic fuzzy number and its arithmetic operation with application on system failure. Exponential operations of intervalvalued intuitionistic.
Research article an intervalvalued intuitionistic fuzzy. Especially, considering an interval valued pythagorean fuzzy element ivphfe is formed by several pairs of interval values, this paper proposes the concepts of score function and accuracy function in the form of two interval numbers which can retain interval valued pythagorean fuzzy information as. To achieve it, we first present some shortcomings of the existing possibility degree method and score function of ifns. Complete ranking of intuitionistic fuzzy numbers sciencedirect. Ye 49 also proposed a novel accuracy function to rank interval valued intuitionistic fuzzy numbers. The novelty of these functions is that they allow the comparison of ivifns by taking into account of the decision makers attitudinal character. Consider that we may utilize interval valued intuitionistic fuzzy numbers ivifns to express uncertain weight information comprehensively in the complex. Qiansheng, a generalized interval valued intuitionistic fuzzy sets theory, advanced in control engineering and information science, vol. Intervalvalued intuitionistic fuzzy multiple attribute group. The hesitant fuzzy concept is merges with interval valued intuitionistic fuzzy number and find the arithmetic operation in.
Firstly, based on the possibility degree of intuitionistic fuzzy values, the possibility degree and divergence degree of ivifvs are defined to provide a new order relation of ivifvs. Request pdf simplified intervalvalued intuitionistic fuzzy sets with intuitionistic fuzzy numbers there has been a growing interest and activity in the field of interval valued intuitionistic. Extension of weighted aggregated sum product assessment with interval valued intuitionistic fuzzy numbers waspasivif. Their definition is given firstly, and the stability of this kind of systems is studied, the relations of interval type2 fuzzy systems and ts fuzzy descriptor systems and fuzzy. Intervalvalued intuitionistic fuzzy number uses membership degree and nonmember ship degree to express a decisionmakers hesitation, which make decisionmaker express hisher opinion in uncertainty decisionmaking environment easily. A study on ranking of trapezoidal intuitionistic fuzzy numbers. The ivifgns are based on the intuitionistic fuzzy sets and interval valued intuitionistic fuzzy.
It reports on cuttingedge research carried out by the founder of the intuitionistic fuzzy sets, prof. The interval valued intuitionistic fuzzy sets have received great attention of researchers because they can comprehensively depict the characters of things. The intervalvalued intuitionistic fuzzy determinant is also defined. Simplified intervalvalued intuitionistic fuzzy sets with. Pdf a comparative study on interval arithmetic operations with. However in some cases the proposed techniques for ranking interval valued intuitionistic fuzzy numbers using a score function or an accuracy function. Firstly, the possibilitydegree and deviationdegree of interval number are used to establish the preference relation of interval valued intuitionistic fuzzy number. New operations over interval valued intuitionistic. To overcome this drawback, in this paper, we have proposed a simplified interval valued intuitionistic fuzzy set sivifs and the corresponding simplified interval valued intuitionistic fuzzy number sivifn which are characterized by two ifns.
Intervalvalued intuitionistic fuzzy envelopment analysis and. Thus, a new accuracy function of an intervalvalued intuitionistic fuzzy number was proposed as follows. In the present paper, we generalize the intuitionistic fuzzy if number to interval valued intuitionistic fuzzy number by defining interval membership and nonmembership functions instead of fixed valued function and hence it will present uncertain situation better than if numbers. Then, we exposit the decision theory and the steps of this. A study on interval valued intuitionistic fuzzy generalized semipreclosed sets 49 is an ivifcs in x and. Dec 21, 2016 this paper puts forward an approach, which rates technical attributes in fuzzy qfd by integrating interval valued intuitionistic fuzzy sets and choquet integral under the case of considering the correlation among customer requirements. Krassimir atanassov, giving a special emphasis to the practical applications of this extension. New generalized interval valued intuitionistic fuzzy numbers. Intervalvalued intuitionistic fuzzy analytic network. Xu 2007h defined the concept of intervalvalued intuitionistic fuzzy number ivifn, and gave some basic operational laws of ivifns. Research article algorithm for target recognition based on. Some limited methods have been presented concerning the ranking of ivif sets in literature.
Intervalvalued multiplicative intuitionistic fuzzy. New operations over interval valued intuitionistic hesitant. Valued ifgn3 ifgn1s and ifgn3s were introduced in 14. Complete ranking on the class of intuitionistic fuzzy interval number was done by geetha et al.
Linguistic intervalvalued intuitionistic fuzzy archimedean. In this paper, the intervalvalued intuitionistic fuzzy matrix ivifm is introduced. This article investigates new score and accuracy functions for ranking interval valued intuitionistic fuzzy numbers ivifns. Then, we have given the operational laws and investigated their desirable properties. As a generalization of fuzzy numbers 20, an intuitionistic. The operations on intervalvalued intuitionistic fuzzy.
Trapezoidaltriangular intuitionistic fuzzy numbers versus. A new multicriteria decisionmaking method for interval valued intuitionistic fuzzy number is proposed by the advantage of intuitionistic fuzzy set and electre method. In case of incomplete and vague data, fuzzy confidence intervals can be used for decision making under uncertainty. To some extent, interval values can better reveal the characteristics of things. A novel arithmetic technique for generalized intervalvalued. When using the proposed algorithm to recognize an unknown target, one should rst establish a target recognition matrix composed of intervalvalued intuitionistic fuzzy numbers. Pdf in this paper, a generalized interval value intuitionistic fuzzy set givifsb is. Assignment problem is consider with intervalvalued intuitionistic fuzzy number on the basis of similarity measure and score function in. A comparative study on interval arithmetic operations with. Intervalvalued intuitionistic fuzzy sets krassimir t. Possibility degree of intervalvalued intuitionistic fuzzy. An interval valued intuitionistic fuzzy set a m a,n a of sris called an. A simple method is to put equal weights on each attribute.
Garg and kumar 2019 proposed linguistic interval valued atanassov intuitionistic fuzzy sets and their application in group decision making problems. Adrian and delia 2014 developed the idea of trapezoidal fuzzy numbers and interval valued trapezoidal fuzzy numbers. This monograph offers a timely guide to the theory and applications of interval valued intuitionistic fuzzy sets. Interval valued intuitionistic fuzzy sets an ivifs 16 18 is an extension of both, the ifs and ivfs. An ivifs of an ivifts x, is said to be an i interval valued intuitionistic fuzzy regular closed set ivifrcs for short if. An optimization model based on the negative ideal solution and maxmin operator, by which the attribute. Application of correlation coefficient to intervalvalued. Intervalvalued intuitionistic fuzzy analytic network process. Interval valued intuitionistic fuzzy envelopment analysis and preference fusion journal preproofs interval valued intuitionistic fuzzy envelopment analysis and preference fusion wei zhou, jin chen, bingqing ding, sun meng pii. Section 3 gives the simplified interval valued intuitionistic fuzzy set sivifs and the simplified interval valued intuitionistic fuzzy number sivifn, and the operations of sivifss. Two important tasks in multiattribute group decisionmaking magdm are to describe the attribute values and to generate a ranking of all alternatives. Reliability analysis of a powerloom plant using interval. This paper addresses the modified arithmetic operations on interval valued intuitionistic fuzzy numbers ivifns for solving interval.
Electre method based on intervalvalued intuitionistic fuzzy. A novel exponential distance and its based topsis method. Pdf new generalized interval valued intuitionistic fuzzy. In the following part, we utilize or to denote an intervalvalued intuitionistic fuzzy number ivifn or an intuitionistic fuzzy number ifn. Ranking of interval valued intuitionistic fuzzy ivif numbers is a most popular and elegant work in the area of decisionmaking of several realworld problems. Formation of an interval valued intuitionistic fuzzy weighted supermatrix. A study on interval valued intuitionistic fuzzy generalized. Due to the advantages of the ivifs, it has been investigated. Possibility degree and divergence degree based method for. Foundation of intervalvalued intuitionistic fuzzy limit. To normalize the supermatrix column vectors, the interval valued intuitionistic fuzzy weighted supermatrix must be constructed. Some generalized einstein aggregation operators based on. The existing shortcomings are overcome by proposing a new possibility degree measure for ifns.
Intervalvalued intuitionistic fuzzy multiple attribute. Section 3 introduces the basic operations for imifns and formulates some aggregation operators for aggregating imifns, serials of properties are also investigated in detail. Interval valued fuzzy sets, possibility theory and. To overcome these shortcomings, this paper aims to develop a new risk evaluation in fmea method. Here we have presented a chart of ifn with transformation rule to fuzzy numbers and interval and real number. The book offers a comprehensive survey of interval valued intuitionistic fuzzy sets. In section 4, we study the interval valued multiplicative intuitionistic fuzzy group. This paper is focused on two types of arithmetic operations on interval valued intuitionistic fuzzy numbers ivifns to solve the interval valued intuitionistic fuzzy multiobjective linear programming problem with pentagonal intuitionistic fuzzy numbers pifns by assuming different. Abstractthis work was motivated by the revealed limitations and drawbacks of the classical definition of interval valued intuitionistic fuzzy set ivifs. In neutrosophic set every element has three membership degrees including a true membership degree t, an indeterminacy membership degree i and a falsity membership degree f independently, which are within the real. Interval valued intuitionistic fuzzy number and its. Intervalvalued intuitionistic fuzzy envelopment analysis.
A superior tool for the first task is linguistic interval valued intuitionistic fuzzy number livifn, and an effective tool for the second task is aggregation operator ao. Electre method based on intervalvalued intuitionistic. To date, nearly ten aos of livifns have been presented. Intervalvalued pythagorean hesitant fuzzy set and its. With respect to multiple attribute decisionmaking problems with interval valued intuitionistic fuzzy information, some operational laws of interval valued intuitionistic fuzzy numbers, correlation and correlation coefficient of interval valued intuitionistic fuzzy sets are introduced. Intuitionistic fuzzy set explanation of a real number. In this paper we define triangular, trapezoidal, pentagonal, hexagonal and octagonal interval valued fuzzy numbers and develop new ranking technique on those fuzzy numbers which are more efficient. It describes in details relations and operations over interval valued fuzzy sets and pairs, and presents original authors findings upon their applications for different purposes. The intervalvalued intuitionistic fuzzy weight vectors are integrated into a weight vector matrix a.
Under these environments, the various researchers pay more attention to aggregate the di. The linguistic intervalvalued intuitionistic fuzzy. Interval valued intuitionistic fuzzy generalized nets of. Intervalvalued fuzzy sets, possibility theory and imprecise. Pdf in a real world situation, whenever ambiguity exists in the modeling of intuitionistic fuzzy numbers ifns, interval valued intuitionistic. Calculation of global priority vectors and weights. Interval valued trapezoidal intuitionistic fuzzy number. To satisfy much more demands from fuzzy decision making problems, we propose a method to solve the magdm problem in which all the information supplied by the decision makers is expressed as interval valued intuitionistic fuzzy decision matrices where each of the elements is characterized by an interval valued intuitionistic fuzzy number, and. In the present paper, two new extensions of the gns, called interval valued ifgn2 and interval valued ifgn4 ifgn2s and ifgn4s will be introduced. Ranking of intuitionistic fuzzy numbers by new distance. This paper puts forward an approach, which rates technical attributes in fuzzy qfd by integrating interval valued intuitionistic fuzzy sets and choquet integral under the case of considering the correlation among customer requirements. The relationship between interval valued fuzzy sets and intuitionistic fuzzy sets is well known see 10. Intervalvalued intuitionistic fuzzy ideal extensions in semiring. Pdf interval intuitionistic fuzzy clustering algorithm.
In application such as weak consistency judgment of an interval valued intuitionistic fuzzy judgment and multiattribute decisionmaking, the comparison operator is needed. Set pair analysis spa theory is the modern uncertainty theory which is composed by the three components, namely identity. Ranking of intuitionistic fuzzy numbers by new distance measure. In the past few years, some scholars have investigated the calculus of intuitionistic fuzzy information, but yet there is no research on the integrals in interval valued intuitionistic fuzzy circumstance. If the intervalvalued intuitionistic fuzzy ideal extension of by equal to intervalvalued intuitionistic fuzzy set for all then is a constant function which is proved in the following proposition. Another key issue for the interval valued intuitionistic fuzzy multiattribute decision making is how to reasonably distribute attributes weights. Intervalvalued trapezoidal intuitionistic fuzzy generalized. The grade of membership of an element xi x in a fuzzy set is represented by real value in. On the basis of the concept of the interval valued intuitionistic fuzzy sets. The operations on interval valued intuitionistic fuzzy values in the framework of dempstershafer theory. Ranking of intervalvalued intuitionistic fuzzy ivif numbers is a most popular and elegant work in the area of decisionmaking of several realworld problems. In the present paper we give a bijection between the set of trapezoidal intuitionistic fuzzy numbers and a subset of interval valued trapezoidal fuzzy numbers and a bijection between. Assignment problem is consider with interval valued intuitionistic fuzzy number on the basis of similarity measure and score function in. Each intervalvalued intuitionistic fuzzy number represents the intervalvalued membership.
The remaining of this paper is organized as follows. By using interval type2 fuzzy systems and fuzzy numbers intuitionistic fuzzy sets, fuzzy numbers intuitionistic fuzzy descriptor systems are proposed in this paper. The objective of this work is to present a novel multiattribute decision making madm method under interval valued intuitionistic fuzzy ivif set environment by integrating a technique for order preference by similarity to ideal solution topsis method. The main aim of this paper is to give a novel method to extend a similarity measure of generalized trapezoidal fuzzy numbers gtfns to similarity measures of generalized trapezoidal intuitionistic fuzzy numbers gtifns and generalized interval valued trapezoidal fuzzy numbers givtfns such that the initial properties to be preserved.
A new multicriteria decisionmaking method for intervalvalued intuitionistic fuzzy number is proposed by the advantage of intuitionistic fuzzy set and electre method. Intervalvalued intuitionistic fuzzy multiple attribute group decision. Firstly, the possibilitydegree and deviationdegree of interval number are used to establish the preference relation of intervalvalued intuitionistic fuzzy number. Hedayati department of mathematics babol university of technology babol iran email. Later on wang and zhang 2009a, b developed the definition of intuitionistic. In addition, a ranking sensitivity analysis with respect to the risk attitude is provided. An intervalvalued intuitionistic fuzzy topsis method. To solve this problem, the concepts of the interval valued multiplicative intuitionistic fuzzy set ivmifs and the interval valued multiplicative intuitionistic fuzzy number ivmifn were introduced by yu et al. Moreover, we intend to develop a new method to solve intervalvalued intuitionistic fuzzy mcdm problems. Intervalvalued intuitionistic trapezoidal fuzzy number and. A new prospect projection multicriteria decisionmaking. The comparison between some intervalvalued intuitionistic fuzzy numbers can not be undertaken because of its limitation.
Intervalvalued intuitionistic fuzzy information aggregation. Interval valued intuitionistic trapezoidal fuzzy number and its application junhong li1. It is worth mentioning the score degree and accuracy degree functions recently developed by xu and chen in 38 to propose an order relation on the set of interval valued intuitionistic fuzzy numbers ivifns. Pdf trapezoidaltriangular intuitionistic fuzzy numbers. Firstly, interval valued intuitionistic fuzzy generalized einstein weighted averaging ivifgewa operator, interval valued intuitionistic fuzzy. Abirami and stephen8 developed a new approach on ranking lr type interval valued fuzzy numbers. The optimal ordered weighted intuitionistic fuzzy quasiaveraging oowifq operator and the continuous oowifq operator are presented to aggregate all the values in an interval intuitionistic fuzzy.
In this paper, we propose a new ranking method of intuitionistic fuzzy number based on distance measure. Section 4 puts forward a series of operational laws of sivifns, including addition, subtraction, multiplication and division operations, etc. Intuitionisticfuzzysetspast,presentandfuture krassimirt. However, this is too simple to deal with all interval valued intuitionistic fuzzy multi. Intervalvalued intuitionistic trapezoidal fuzzy number. The judgment matrices between the clusters are constructed, and the interval valued intuitionistic fuzzy normalized weight vector is obtained, as shown in table 2. In recent decades, several types of sets, such as fuzzy sets 2, interval valued fuzzy sets 3, intuitionistic fuzzy sets 4, 5, interval valued intuitionistic fuzzy sets 6, type 2 fuzzy. An intervalvalued intuitionistic fuzzy topsis method based. Introduction hesitant fuzzy information under confidence levels, xia et al. First, the extended hamacher tnorm and snorm, which are applicable to linguistic information environment, are applied to define the linguistic interval valued intuitionistic fuzzy hamacher operational laws. First, this paper converts linguistic evaluation information into corresponding interval valued intuitionistic fuzzy numbers ivifns to effectively address the uncertainty and vagueness of the information. As a supplementation, the exponential operational law of intuitionistic fuzzy numbers has been defined. Intervalvalued intuitionistic fuzzy confidence intervals.
The operational laws of intuitionistic fuzzy numbers are useful in dealing with the problems under intuitionistic fuzzy circumstances. The hesitant fuzzy concept is merges with intervalvalued intuitionistic fuzzy number and find the arithmetic operation in. Intervalvalued intuitionistic fuzzy todim sciencedirect. Ye26 also proposed a novel accuracy function to rank interval valued intuitionistic fuzzy numbers. Subsequently in interval valued intuitionistic fuzzy magdm, an intuitionistic fuzzy linear programming model is constructed to derive decision makers weights. Simplified intervalvalued intuitionistic multiplicative. Fuzzy numbers intuitionistic fuzzy descriptor systems.
Pdf on feb 18, 2018, ezzatallah baloui jamkhaneh and others published new generalized interval valued intuitionistic fuzzy numbers find, read and cite all the research you need on researchgate. The ivif todim method has been investigated on tw o. Fuzzy number ifn seems to suitably describe an ill. A risk attitudinal ranking method for intervalvalued.
Multiattribute decisionmaking, intervalvalued intuitionistic sets. Simplified intervalvalued intuitionistic fuzzy integrals. From a geometric viewpoint, the expectation and expectant score of an. Generalized intervalvalued neutrosophic graphs type1. This paper addresses the modified arithmetic operations on interval valued intuitionistic fuzzy numbers ivifns for solving interval valued intuitionistic fuzzy linear programming problem iviflpp with hexagonal intuitionistic fuzzy numbers by. Technical attributes ratings in fuzzy qfd by integrating. To expand its application, new possibility degree functions of interval valued intuitionistic fuzzy numbers were proposed. Many variants of these mathematical objects exist, under.
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